If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as

V=5000 (1-1/50*t)^2 0⤠t ⤠50.

1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)

a. 5 min
b. 10 min
c. 20 min
d. 50 min

2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?

Answer:

2(1)+y =1 for × intercept

2x+(1)=1 for y intercept

Answer:

[tex]A" = (7,-2)[/tex]

[tex]B" = (10,0)[/tex]

[tex]C"= (12,-3)[/tex]

Step-by-step explanation:

Given

[tex]A = (4,2)[/tex]

[tex]B = (7,0)[/tex]

[tex]C =(9,3)[/tex]

a: Reflect over x-axis

The rule of this is:

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]A' = (4,-2)[/tex]

[tex]B' = (7,0)[/tex]

[tex]C' = (9,-3)[/tex]

b: Shift 3 units left

The rule of this is:

[tex](x,y) \to (x+3,y)[/tex]

So, we have:

[tex]A" = (4+3,-2)[/tex]

[tex]A" = (7,-2)[/tex]

[tex]B" = (7+3,0)[/tex]

[tex]B" = (10,0)[/tex]

[tex]C"= (9+3,-3)[/tex]

[tex]C"= (12,-3)[/tex]

Answer:

the domain is ALL reals numbers except ZERO

- ∞ < x < 0    ∪   0 <  x < ∞

Step-by-step explanation:

Answer:

(-∞,0) ∪ (0,∞), {x|x≠0}

Step-by-step explanation:

I think this is it. Im not completely sure though

Answer:

a. The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

b. $ 16.7

Step-by-step explanation:

a. How many pounds of each are needed in order to minimize the cost and still meet the minimum requirements?

Let c represent the carbohydrate units and p the protein units.

For the meat portion M, we have 2 units of carbohydrates and 2 units of protein per pound. So, M = 2c + 2p

For the cheese portion K, we have 3 units of carbohydrates and 1 units of protein per pound. So, K = 3c + p.

Let x be the number of pounds of meat required and y be the number of cheese pounds required. The total number of pounds required is T

So, we have xM + yK = x(2c + 2p) + y(3c + p)

= 2xc + 2xp + 3yc + yp

= 2xc + 3yc + 2xp + yp

= (2x + 3y)c + (2x + y)p

Since the required number of units, R is 12 units of carbohydrates and 8 units of protein, we have R = 12c + 8p

Since T = R, we have

(2x + 3y)c + (2x + y)p = 12c + 8p

Equating coefficients, we have

2x + 3y = 12 (1) and 2x + y = 8 (2)

Subtracting (2) from (1), we have

2x + 3y = 12 (1)

-

2x + y = 8 (2)

2y = 4

y = 4/2

y = 2

Substituting y = 2 into (2), we have

2x + y = 8

2x + 2 = 8

2x = 8 - 2

2x = 6

x = 6/2

x = 3

Since x = 3 and y = 2

The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

What is the minimum cost?​

Since meat costs $3.70 per pound and the cheese costs $2.60 per pound and we have 3 pounds of meat and 2 pounds of cheese, the total cost of meat is C = $3.70/pound × 3 pounds = $ 11.1.

The total cost of cheese is C' = $2.60/pound × 2 pounds = $ 5.2.

So, the minimum cost C" = C + C' = $ 11.1 + $ 5.2 = $ 16.7

Answer:

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

3x+2y<11 doesn't have a y-intercept of 6 and doesn't have a x-intercept of 4.

2x-y<9 is not the same direction as 3x+2y<11.

Answer:

3 seconds

Step-by-step explanation:

First, let's calculate the approximate speed of light.

3 · 10^14 = 3 · 100,000,000,000,000

              = 300,000,000,000,000

Approximately, light travels 300,000,000,000,000 centimeters per second.

Now, let's simplify 9x10^14.

9 · 10^14 = 9 · 100,000,000,000,000

              = 900,000,000,000,000

To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.

900,000,000,000,000/300,000,000,000,000 = 3

Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.

It will take 3 seconds to cover the distance of 9×10¹⁴ cm.

We use the scientific notation of numbers to write very large numbers in compact form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given the speed of light s approximately 3×10¹⁴ cm/sec.

∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.

We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.

learn more about scientific notation here :

https://brainly.com/question/18073768

#SPJ2

Answer: guess it your self

Step-by-step explanation:

Answer:

The number of devices infected with the virus increases by 24% each day.

Step-by-step explanation:

Have a nice day! ♡

Answer: 7 / 8 should be added

Step-by-step explanation:

Let x be the number that should be added

Write the equation

-3/2 + x = -5/8

Add -3/2 on both sides

-3/2 + x + 3/2 = -5/8 + 3/2

x = -5/8 + 3/2

Change the denominator of 3/2 to 8 in order to do addition

x = -5/8 + 12 / 8

x = 7 / 8

Hope this helps!! :)

Please let me know if you have any questions

x= 55°

according to the picture .........

Answer:

2

Step-by-step explanation:

Let x represent the total number of people. Let C represent those that like cake and let I represent those that like ice cream. Given:

C = (1/4)x = 0.25x, I = 0.5x, (C ∪ I)' = 12, C' = 20

Therefore:

C ∩ I' = C' - (C ∪ I)' = 20 - 12 = 8

C ∩ I = C - C ∩ I' = 0.25x - 8

C' ∩ I = I - C ∩ I = 0.5x - (0.25x - 8) = 0.25x + 8

The total students = (C ∩ I) + (C' ∩ I) + (C ∩ I') + (C ∪ I)'

x = 0.25x - 8 + 0.25x + 8 + 8 + 12

x = 0.5x + 8 + 12

x = 0.5x + 20

0.5x = 20

x = 40

Students that liked both = C ∩ I = 0.25(40) - 8 = 2

Answer:

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

150 guests booked:

This means that [tex]n = 150[/tex]

85% of booked guests show up for their room.

This means that [tex]p = 0.85[/tex]

Is the normal approximation suitable:

[tex]np = 150(0.85) = 127.5[/tex]

[tex]n(1-p) = 150(0.15) = 22.5[/tex]

Both greater than 10, so yes.

Mean and standard deviation:

[tex]\mu = E(X) = np = 150*0.85 = 127.5[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{150*0.85*0.15} = 4.3732[/tex]

Find the probability that if the motel books 150 guests, not enough seats will be available.

More than 140 show up, which, using continuity correction, is [tex]P(X > 140 + 0.5) = P(X > 140.5)[/tex], which is 1 subtracted by the p-value of Z when X = 140.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{140.5 - 127.5}{4.3732}[/tex]

[tex]Z = 2.97[/tex]

[tex]Z = 2.97[/tex] has a p-value of 0.9985.

1 - 0.9985 = 0.0015.

0.0015 = 0.15% probability that if the motel books 150 guests, not enough seats will be available.

Answer:

C

Step-by-step explanation:

Just trust

Answer:

C

Step-by-step explanation:

I did the assignment in edge and got it right.

Proof:

Answer:

answer is 12

Step-by-step explanation:

gcf = 3

lcm = 180

let 45 be y

let unknown be X

to get x

X=( lcm * gcf) / y

X=(180*3)/45

X=(540)/45

X=12

the other number is 12

Answer:

8 months 11 days 1 year

dy/dx = 4 + √(y - 4x + 6)

Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes

dv/dx + 4 = 4 + √v

dv/dx = √v

which is separable as

dv/√v = dx

Integrating both sides gives

2√v = x + C

Get the solution back in terms of y :

2√(y - 4x + 6) = x + C

You can go on to solve for y explicitly if you want.

√(y - 4x + 6) = x/2 + C

y - 4x + 6 = (x/2 + C )²

y = 4x - 6 + (x/2 + C )²

Answer:

a first degree equation

Answer:

-9

Step-by-step explanation:

-2 3 + |7| - 4 · 2

I assume -2 3 means -2^3.

-2^3 + |7| - 4 · 2 =

= -8 + 7 - 8

= -1 - 8

= -9

Answer:

-9

Step-by-step explanation:

-2^ 3 + |7| - 4 · 2

Parentheses first and an absolute value is considered parentheses

-2 ^3 + 7 - 4 · 2

Then exponenets

Since the sign is outside of the exponent it is considered multiplication

-1 * (2^3)+ 7 - 4 · 2

-1 *8 + 7 - 4 · 2

Then multiply

-8 +7 -8

Then add and subtract from left to right

-1-8

-9

explainion:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.

Answer:

B.

Step-by-step explanation:

The answer is B.

Answer:

$25.80

Step-by-step explanation:

First, let's find the cost of one bag of chip:

10.32/8 = 1.29

If one bag costs $1.29, simply multiply the number of bags (20) by 1.29

1.29 x 20 = 25.80

               = $25.80

Answer:

25.80

Step-by-step explanation:

We can use a ratio to solve

8 bags             20 bags

-------------   = ----------------

10.32               x dollars

Using cross products

8x = 10.32 * 20

8x =206.40

Divide each side by 8

8x/7 = 206.40/8

x =25.80

Answer:

0.002

Step-by-step explanation:

2 in 4.502 is in the thousandths place

Value is 0.002

Answer:

8. 72% × 850

= 72/100 × 850

= 72 × 8,5

= 612 ( b )

9. Poin B = 4 ( b )

Answer:

8. B

9. B

10. C

Step-by-step explanation:

8. To find 72% of 850, you would multiply 0.72 x 850. When you do that, it gives you 612.

9. B is on the number 4.

10. The expression is asking, "What is the absolute value of 28?". Absolute value means that the number inside will always be positive. For example, if it was -28, the absolute value would turn to 28. Since the question has 28 already positive, there is no change, so the answer would be 28.

Answer:

The  proportions of the diameters that are greater than 25.4 millimeters is 5%.

Step-by-step explanation:

Given;

mean of the normal distribution, m = 25.1 millimeters

standard deviation, d = 0.08 millimeter

1 standard deviation above the mean = m + d = 25.1 + 0.08 = 25.18

2 standard deviation above mean =  m + 2d = 25.1 + 2(0.08) = 25.26

3 standard deviation above the mean = m + 3d = 25.1 + 3(0.08) = 25.34

4 standard deviation above the mean = m + 4d = 25.1 + 4(0.08) = 25.42

To obtain a diameter greater than 25.4, we select data after 4 standard deviation above the mean.

Data within 4 standard deviation above the mean is 95%

Data outside 4 standard deviation above the mean is 5%

Therefore, the  proportions of the diameters that are greater than 25.4 millimeters is 5%.

A = 10,00,000

P = 10,000

T = 2

1000000 = 10000(1+r/100)^2

1000000 = 10000((100 + r)/100)^2

1000000 = 10000× 100 + r/100 × 100 + r/100

1000000 = 10000 + r^2

1000000 - 10000 = r^2

990000 = r^2

√99000 = r

Quadratic Equation

10000(1+r/100)^2

Answer:

=3/8×1 1/2×1 1/2

=3/8 ×3/2×3/2                                            ∴ 1 1/2 =2×1+1/2=3/2

=27/32                                                        ∴3×3×3=27   ∴8×2×2=32

Answer:

it should be letter c

Step-by-step explanation:

I hope this help

Answer:

Step-by-step explanation:

One way of solution is to plot the lines and points and confirm the answer visually.

See attached.

Another way is to substitute the coordinates and verify if they satisfy both of the inequalities.

Each of the methods gives us the correct answer choice of D.

Answer:

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they agree with the claim, or they do not. The probability of an adult agreeing with the claim is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

75% of adults believe that an unattractive smile hurts career success.

This means that [tex]p = 0.75[/tex]

Suppose that 25 adults are randomly selected.

This means that [tex]n = 25[/tex]

What is the probability that 15 or more of them would agree with the claim?

This is:

[tex]P(X \geq 15) = 1 - P(X < 15)[/tex]

In which:

[tex]P(X < 15) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 13) + P(X = 14)[/tex]

14 is below the mean, so we start below and go until the probability is 0. Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 14) = C_{25,14}.(0.75)^{14}.(0.25)^{11} = 0.0189[/tex]

[tex]P(X = 13) = C_{25,13}.(0.75)^{13}.(0.25)^{12} = 0.0074[/tex]

[tex]P(X = 12) = C_{25,12}.(0.75)^{12}.(0.25)^{13} = 0.0025[/tex]

[tex]P(X = 11) = C_{25,11}.(0.75)^{11}.(0.25)^{14} = 0.0007[/tex]

[tex]P(X = 10) = C_{25,10}.(0.75)^{10}.(0.25)^{15} = 0.0002[/tex]

[tex]P(X = 9) = C_{25,9}.(0.75)^{9}.(0.25)^{16} \approx 0[/tex]

Then

[tex]P(X < 15) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0002 + 0.0007 + 0.0025 + 0.0074 + 0.0189 = 0.0297[/tex]

And

[tex]P(X \geq 15) = 1 - P(X < 15) = 1 - 0.0297 = 0.9703[/tex]

0.9703 = 97.03% probability that 15 or more of them would agree with the claim.

Step-by-step explanation:

well, what does the word "constant" tell you ?

e.g. "this is a constant reminder of ..."

a constant is steady and unchanging. always the same.

so, what could be the constant part/term in the expression ?

-3xy ? is that always the same value ? no matter what values you assign to x, y (and whatever other variables there might be in the system)?

or

10 ? is that always the same value, no matter what values are assigned to x, y, ... ?

there are no other parts/terms I can see here.

so, please use your common sense and pick the right one. you can do that !

this is so simple. to outright write the answer to this feels like an offense. also against your own intelligence.